Does Friedrich Hayek believe man stumbled upon the price system?
Yes, Hayek does believe that people simply stumbled upon the price system. He says so in so many words when he says
The price system is just one of those formations which man has learned to use ... after he had stumbled upon it...
What Hayek is saying is that people did not realize exactly how useful prices would be. When they started to put prices on things, they did not know how much information could be transmitted by prices.
Hayek believes that prices do a great job of transmitting information. They can tell us things like how much demand there is for a product or how high the supply of that product is. People who need the product or make the product can then plan accordingly.
If it were not for prices, economics would move much more slowly and much less efficiently. However, when people first discovered the idea of pricing, they did not realize that it was as useful as it really is.